GIVEN DI FFERFNTIAL EQUATIONFIND A ONE PARAMETER FAMILYSOLUTIOALL OR WHICH ARE SOLU 7 (SNSTHEIN (TIAL VA LUE PROBLEMxy'=y ;yo)=0wit Y is RS NOT ACONTRADICTION FEXISTENCE AND UNIQUENESS TiHEOREMFORFIRST ORDERODE'S ?

Name: GIVEN DI FFERFNTIAL EQUATIONFIND A ONE PARAMETER FAMILYSOLUTIOALL OR
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Description: GIVEN DI FFERFNTIAL EQUATIONFIND A ONE PARAMETER FAMILYSOLUTIOALL OR WHICH ARE SOLU 7 (SNSTHEIN (TIAL VA LUE PROBLEMxy'=y ;yo)=0wit Y is RS NOT ACONTRADICTION FEXISTENCE AND UNIQUENESS TiHEOREMFORFIRST ORDERODE'S ?

Given, xy'=y Then, xdydx=yor,dyy=dxdx

Answered: GIVEN DI FFERFNTIAL EQUATION FIND A ONE…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

GIVEN DI FFERFNTIAL EQUATION
FIND A ONE PARAMETER FAMILY
SOLUTIO
ALL OR WHICH ARE SOLU 7 (SNS
THE
IN (TIAL VA LUE PROBLEM
xy'=y ;
yo)=0
wit Y is RS NOT A
CONTRADICTION F
EXISTENCE AND UNIQUENESS TiHEOREM
FOR
FIRST ORDER
ODE'S ?

Expert Solution

Step 1

Given,

$x y' = y$

Then,

$\begin{array}{rcl} x \frac{d y}{d x} & = & y \\ o r, \frac{d y}{y} & = & \frac{d x}{d x} \end{array}$

Step 2

Integrating,

$\log (y) = \log (x) + \log (c) o r, y = c x$

where, $c$ is a constant.

Step 3

$y (0) = 0$

Then, $c$ can be any number . For all values of c, this initial value will be satisfied.

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